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We present detailed numerical and experimental investigation of thin-film organic solar cells with a micro-textured light management foil applied on top of the front glass substrate. We first demonstrate that measurements of small-area laboratory solar cells are susceptible to a significant amount of optical losses that could lead to false interpretation of the measurement results. Using the combined optical model CROWM calibrated with realistic optical properties of organic films and other layers, we identify the origins of these losses and quantify the extent of their influence. Further on, we identify the most important light management mechanisms of the micro-textured foil, among which the prevention of light escaping at the front side of the cell is revealed as the dominant one. Detailed three-dimensional simulations show that the light-management foil applied on top of a large-area organic solar cell can reduce the total reflection losses by nearly 60% and improve the short-circuit current density by almost 20%. Finally, by assuming realistic open-circuit voltage and especially the realistic fill factor that deteriorates as the absorber layer thickness is increased, we determine the optimal absorber layer thickness that would result in the highest power conversion efficiency of the investigated organic solar cells.
© 2017 Optical Society of America
1. Introduction
Further advances and scientific breakthroughs in photovoltaic technology are crucial for meeting the global demand for sustainable energy. For the past decade, we have been witnessing a plethora of research efforts on all levels of photovoltaics with the common goal of reducing the manufacturing costs and further increasing the power conversion efficiency. In this respect, optical modelling and simulation has been recognized as an indispensable tool for efficient design and optimization of novel solar cell structures and their optical performances [1,2]. However, as the solar cell structures become ever more complex, so must the optical models that are used for their analysis. Nowadays, it is common for photovoltaic devices to feature both thin layers (coherent light propagation) and thick layers (incoherent light propagation) with both nano-scale textures (diffraction effects) and micro-scale textures (refraction effects) applied to the interfaces [3–5]. To treat such structures, combination of different modelling techniques is required in which different optical models and methods are used in conjunction to analyse light interaction with different components/regions of the investigated device [1,6,7]. The reliability of such modelling depends on the chosen numerical methods, the description of the simulation domain (layer thicknesses, texture profiles, boundary conditions), and the accuracy of the input parameters (illumination conditions, optical properties of the materials).
While optical modelling can be the key in developing promising novel solar cell concepts, realistic prototype devices inevitably need to be fabricated and experimentally characterized. This step, however, introduces additional variables: First, the chosen characterization method may be prone to a certain amount of errors. And second, since the prototype lab-fabricated solar cells are typically extremely small, on the order of a few square millimetres, this limited cell size can also impose its own artifacts that otherwise wouldn’t exist on a larger scale (e.g. module application). Since these two typically negative effects can obscure those introduced by the investigated solar cell concept, it is therefore of paramount importance to understand and properly evaluate them.
In this work, we present the complete process of detailed optical modelling of thin-film organic solar cells including optical characterization and acquisition of realistic input parameters. Organic solar cells show potential due to their low cost, mechanical flexibility, and applicability to roll-to-roll fabrication [8–10]. We choose an example cell based on the pDPP5T-2:PC60BM absorber material, however the presented methodology and the main conclusions are also relevant for any other absorber type and, in fact, also many other thin-film technologies, including perovskite solar cells. Special attention is paid to proper modelling of the solar cell structure with a micro-textured light management foil applied on top of the front glass substrate to improve its performance, as has been indicated in our previous work [11].
As the first step of the process, we determine the complex refractive indices of the solution-processed materials. For this purpose, we apply the reflectance-transmittance method that does not require any pre-defined dispersion function models [12,13]. Then, by means of experimental techniques as well as advanced optical simulations using the optical simulator CROWM (Combined Ray Optics / Wave Optics Model) [14,15], detailed optical analysis of standalone micro-textured light management foil as well as the complete organic solar cell is performed. We focus on answering the following two questions: how does the light management foil improve the overall performance of the organic solar cell, and how (and to which extent) do the conditions and artifacts of the measurement system affect the experimental results. We demonstrate that advanced optical modelling based on CROWM is crucial for obtaining both answers, which are discussed in detail.
In the last part of our work, we focus on identifying the optimal absorber layer thickness of the solar cell that renders the highest amount of photocurrent. Due to the coherent nature of light propagation in the thin absorber layer, the optimal thickness depends heavily on all other parameters of the device, including the absence or presence of the micro-textured light management foil. We use optical simulations to determine the optimal absorber layer thickness in both cases. However, since varying the absorber layer thickness in reality also affects the fill factor of the solar cell [16], we also calculate the power conversion efficiency by taking the realistic fill factor values into account. Thus, the realistic optimal absorber layer thickness is revealed for both the bare solar cell and the cell with the micro-textured light management foil.
2. Experimental
The organic solar cell was fabricated as follows [17]: a 1 mm thick float glass substrate covered with a 360 nm thick layer of indium tin oxide (ITO) was first cleaned by ultra sonication in acetone and isopropanol for 10 min each. On the cleaned ITO substrate, 70 nm thick poly(3,4-ethylenedioxythiophene) doped with poly(styrene sulfonate) (PEDOT:PSS) hole conductor was doctor bladed from its diluted solution (1:3 vol. % in isopropanol) and dried at 140 °C for 5 min. Then, 135 nm thick photoactive blend of diketopyrrolopyrrole (DPP) based polymer (pDPP5T-2) and [6,6]-phenyl-C60-butyric acid methyl ester (PC60BM) (1:2 wt. %) was coated from a mixed solvent of dichlorobenzene and chloroform (1:9 vol. %) at a total concentration of 24 mg/mL. The device fabrication was completed by thermal deposition of 15 nm thick calcium (Ca) and 85 nm thick silver (Ag) layers on top of the photoactive absorber layer. The schematic structure of the fabricated solar cell is presented in Fig. 1.
Fig. 1 Schematic structure of the fabricated organic solar cell based on the pDPP5T-2:PC60BM photoactive absorber material. In the case of textured cell, the micro-lens array (MLA) was laminated on top of the front glass substrate (textured surface at front). Also indicated are the partial structures A and B that were used in the simulations.
For the purpose of light management in the fabricated organic solar cell, a commercial micro-lens array (MLA) HT-MLA-09 (Holotools GmbH, Germany) was employed. The MLA consists of a 0.5 mm thick polyethylene terephthalate (PET) substrate covered by 100 µm thick photosensitive lacquer on which a convex parabolic hexagonal honeycomb micro-texture was realized by means of interference lithography, as shown in Figs. 2(a) and 2(b). The period, P, and the height, h, of the texture are 9 µm and 5.5 µm, respectively, which is close to the optimal texture shape that we have determined in a previous work [11]. In the experiment, the MLA was laminated on top of the organic solar cell, as shown in Fig. 1. For the purpose of optical simulations, the ideal texture profile using the same P and h values was generated by a computer program. The computer-generated profile is presented in Fig. 2(c) and shows very good agreement with the realistic texture.
Fig. 2 Top-down (a) and side-view (b) SEM images of the parabolic MicroLens Array HT-MLA-09 (images courtesy of Holotools GmbH, Germany). Also shown is the computer-generated texture (c) that was used in the simulations (the period P = 9 μm and height h = 5.5 μm were extracted from the SEM images as indicated).
To determine the complex refractive indices of the solution-processed materials, single flat layers of PEDOT:PSS and pDPP5T-2:PC60BM in thicknesses between 50 nm and 200 nm were deposited on top of a 1 mm thick float glass substrate using doctor blade coating. The thicknesses of the dried single layers were measured using the Nikon Eclipse L150 confocal microscope.
To measure the total reflectance, R, and the total transmittance, T, of the single thin layers on glass as well as the MLA, we used the PerkinElmer Lambda 950 spectrophotometer (PerkinElmer, MA, USA) equipped with a 150 mm integrating sphere with a photomultiplier and a PbS detector. The single thin layers on glass were measured in the range of 300 – 900 nm, illumination was applied from the layer side. The MLA was measured from both sides in the range of 300 – 800 nm.
The external quantum efficiency, EQE, spectra of the organic solar cell were measured using a Varian CARY 500 Scan spectrometer with a tungsten light source. A silicon photodiode served as the reference for calibration of the system prior to the measurements.
3. Optical modelling
To perform all optical simulations of standalone MLA samples and complete organic solar cells presented in this work, we employed the optical simulator CROWM (Combined Ray Optics / Wave Optics Model) [14,15]. It is based on the combination of two fundamentally different numerical methods for the analysis of light propagation, which are applied separately to different parts of the simulated device, as shown in the (simplified) structure in Fig. 3. The incident medium, the transmission medium, and each “thick” layer (typically > 10 µm) in the structure are treated by means of three-dimensional ray tracing (RT) [18,19], where the propagation angles and the intensities of light rays are governed by the geometric optics approach. Arbitrary two-dimensional micro- or millimetre-scale textures can be applied on the surfaces of these thick layers. On the other hand, the “thin” layers (or stacks of thin layers) in between the ray-traced media are treated by means of fully-coherent one-dimensional transfer matrix formalism (TMF) [20], taking all interference effects into account. Further details on the basic model principles can be found in [14].
Fig. 3 Schematic principle of the combined modelling approach implemented in CROWM (shown in 2D and with only one thick layer for simplicity). Ray tracing (RT) applied to thick layers (incoherent light propagation) is iteratively coupled to transfer matrix formalism (TMF) applied to thin layers (coherent light propagation).
The primary input parameters of a CROWM simulation are the incident illumination spectrum and polarization (relative to a global coordinate system), the complete structure definition (layer thicknesses, texture parameters, etc.), and the wavelength-dependent complex refractive indices of the materials. The primary output parameters are the wavelength-dependent total reflectance, the total transmittance, and the absorptance within each layer of the device.
The optical model that has been recently updated with a number of additional features (current version 3) enables accurate simulation under a wide range of conditions. First, it is possible to adapt the parameters of the incident illumination, such as the angle of incidence, the spatial distribution of the incident rays (e.g. parallel, spherical, Lambertian), or the area/width of the incident beam. Different boundary conditions can be applied to the lateral borders of the simulation domain, which enables simulation of infinite as well as finite-area devices. Further on, as will be shown later, it is possible to obtain the angular intensity distribution, AID, of diffused light inside any ray-traced medium. And finally, the model can also be extended to the case of nano-textured interfaces between the thin layers when needed. In this case, the thin-film stacks can be treated by models other than TMF, for example by means of the three-dimensional rigorously-coupled wave analysis (RCWA), while still being coupled to the ray-tracing algorithm applied to the ray-traced media.
All of the features mentioned above enable accurate simulation of complex optoelectronic devices. The versatility of the combined optical model has already been demonstrated for simulation of different types of solar cells [21,22], as well as for more advanced optical concepts such as phosphor-based luminescent down-shifting layers and their applications [23]. With no less importance, however, we will also demonstrate in the following that the combined optical modelling approach is beneficial for the understanding and accurate evaluation of measurement results which may in some cases lead to false interpretation.
4. Results and discussion
4.1 Determination of complex refractive indices
The wavelength-dependent complex refractive index of a material, n(λ) – i·k(λ), presents one of the primary input parameters for optical simulations. Its accurate acquisition is therefore of great importance for reliable simulations. In the case of organic solution-processed materials, we found out that the reflectance-transmittance (RT) method [12] is especially suitable. It is simple, fast, can be applied to thin and thick layers, and delivers results directly without the need for fitting to the (often unknown) dispersion models (e.g. as is the case in ellipsometry [24]).
In this work, n&k parameters of solution-processed PEDOT:PSS and pDPP5T-2:PC60BM, as well as the ITO layer and the glass and PET substrates, were determined using an RT method [13]. For greater accuracy, each solution-processed material was deposited multiple times in different thicknesses. As an example, the results of n&k determination for PEDOT:PSS are presented in Fig. 4 for the case of 72 nm thick (white circles) and 107 nm thick (grey diamonds) layers. Since the dispersion of n should be continuous, smooth, single-valued and is expected to be larger than 1, the final realistic n values and the corresponding k values can be extracted from the averaged results as shown by the full red line. The final complex refractive index data for all five materials obtained by the RT method are summarized in Fig. 5.
Fig. 4 Determination of the real (a) and imaginary (b) parts of the complex refractive index of PEDOT:PSS by using the RT method. The final (physically realistic) solution can be extracted from the multiple solutions that are obtained from the R and T measurements for each of the two samples (white circles for the 72 nm and grey diamonds for the 107 nm thick layer).
Fig. 5 Calculated dispersion curves of the real (a) and imaginary (b) parts of the complex refractive indices of the materials employed in the fabricated organic solar cell.
4.2 Simulation of the micro-lens array
We begin our studies by numerical and experimental investigation of the standalone MLA sample (HT-MLA-09). The purpose of this step is to determine the optical transmittance of the MLA, which is crucial for its solar cell application, and also to observe how the measured and the simulated results compare to each other.
For the purpose of simulations, only the ray-tracing component of the combined optical model was employed, since there are no thin layers present in the sample. The complex refractive index of the photosensitive lacquer was assumed to be the same as that of PET. Two simulations were performed separately with the illumination being incident on (i) the textured side (“normal” orientation) and (ii) on the flat side of the MLA sample (“inverted” orientation). Initially, both an infinite sample size and an infinite illumination beam size were assumed in the simulations.
The measured (symbols) and the simulated (dashed blue lines) total transmittance results are presented in Fig. 6. Apart from the short-wavelength region, where the discrepancies between the results can mostly be attributed to the unknown k parameter of the commercial photosensitive lacquer, we observe a very good agreement in the case of “normal” orientation. In the case of “inverted” orientation, however, agreement is poor; simulations seem to greatly overestimate the amount of transmitted light through the sample. The substantial relative error compared to the measurements is about 20%, and this may lead us to conclude that the combined optical model cannot be reliably employed for this case. We found out, however, that this conclusion is ill-founded, as the error in fact lies in the measurement results that require proper interpretation.
Fig. 6 Measured (symbols) and simulated (lines) total transmittance of the MLA sample (measurements from both sides). Simulations assuming infinite geometry are plotted as dashed blue lines, whereas full red lines show simulations that take the realistic sample, beam and measurement system geometry into account.
The illustration in Fig. 7(a) shows schematically the optical situation of measuring a scattering sample using the integrating sphere. Due to the geometry constraints of the measurement system, only a part of the total transmitted light can be efficiently coupled into the integrating sphere, while two important origins of losses can be identified (also indicated in Fig. 7(a)): first, due to large angles of propagation caused by a surface texture, an amount of the transmitted scattered light is lost by “missing” the aperture of the integrating sphere. And second, due to the realistic thickness of the walls of the integrating sphere (~1 mm in our case), an amount of the transmitted scattered light is lost by being obstructed by this boundary and not being able to efficiently couple into the sphere. Together, these two effects can result in a significant amount of the transmitted scattered light that cannot be detected by the detector and, therefore, does not contribute to the measured T results. However, it is difficult to measure these optical losses experimentally.
Fig. 7 Schematic representation of (a) transmittance measurement in the integrating sphere, and (b) external quantum efficiency measurement. A substantial amount of light can be lost due to the limited dimensions of the sample, incident light beam, aperture of the integrating sphere, and the cell back contact, which all contribute to lower measured values.
Therefore, to evaluate the extent to which the constraints of the measurement system affect the results, we upgraded the combined optical model CROWM to enable complete adherence to the realistic measurement system geometry. Thus, we were able to perform simulations that take the actual size of the incident beam, the size of the MLA sample, the size of the aperture, and the thickness of the walls of the integrating sphere fully into account. The simulated T results are plotted in Fig. 6 as full red lines. Very good agreement between the simulations and measurements can now be observed for both cases. On the one hand, these realistic simulation results further verify the validity of the combined optical model, while on the other hand they also help to properly interpret the measured data and assess the amount of optical losses which otherwise could not be determined experimentally. In the case of the MLA sample in the “inverted” orientation with the textured side pointing towards the integrating sphere, we can conclude that measurement results underestimate the actual transmittance of the sample by about 15% due to the unavoidable constraints of the measurement system. Therefore, one should pay attention to possible constraints in this manner also when characterizing other devices using the integrating sphere, including solar cells and PV modules (e.g. total reflectance measurements).
Finally, from the results shown in Fig. 6, a significant difference between the “normal” and the “inverted” MLA orientation can be observed. Much more light is lost during the measurement in the “inverted” case (about 15%) compared to the “normal” one (below 1%). To further investigate this conclusion, we employed the ability of the combined optical model to determine the angular intensity distribution, AID, of the scattered (refracted) light inside any ray-traced medium; in our case, we are interested in the medium in transmission (i.e. direction of propagation of the transmitted light). In general, AID is a function of both the zenith angle, θ, and the azimuth angle, φ. However, since we are focusing only on the zenith angle dependency (i.e. scattering of light into angles away from the specular direction), we integrated the results over all azimuth angles in all cases. Further on, since the texture features of the MLA are large (geometric optics regime) and there is little dispersion of the refractive indices, especially for the materials in MLA, AID is expected to be mostly wavelength independent. Therefore, we determined AID only at a single wavelength λ = 700 nm.
The simulated AID results as a function of the zenith angle (specular direction: θ = 0°) for different cases are presented in Fig. 8. All the results are normalized, and the absolute total transmittance values at the selected wavelength are given next to each AID curve. The left-hand side of the figure shows the results for the “normal” orientation of the MLA, while the right-hand side shows the results for the “inverted” orientation. First, we simulated an isolated single textured interface: air/MLA (“normal” orientation) and MLA/air (“inverted” orientation). The results are plotted as black lines. It can be seen that for the “inverted” case, there is less transmitted light (lower T), yet the light is scattered into much larger angles. Both can be attributed to the fact that the refractive index of the incident medium is in this case (MLA) larger than the refractive index of the medium in transmission (air). On the one hand this leads to a narrower escape cone at the textured MLA/air interface due to the effect of total internal reflection, while on the other hand it also results in larger angles of refraction into the medium in transmission. Then, we also simulated the entire standalone MLA sample: air/MLA/air. The results are plotted as blue lines. Again, we can see that the “inverted” MLA orientation scatters light into much larger angles away from the specular direction. We conclude that this is also the main reason why measurements of the “inverted” MLA sample oriented with the textured side towards the integrating sphere suffer from much more pronounced optical losses; since the transmitted light is scattered into much larger angles in this case, its coupling into the integrating sphere is less efficient.
Fig. 8 Normalized angular intensity distribution of the transmitted light at λ = 700 nm for: i) single air/MLA interface (black), ii) standalone MLA sample (blue), and iii) top part of the solar cell with the MLA (red). The plots are shown for the “normal” orientation (left; texture on the top surface), and the “inverted” orientation (right; texture on the bottom surface).
4.3 Simulation of the complete organic solar cell
We continue with numerical and experimental investigation of the complete organic solar cell. While the main purpose is to determine the potential of the MLA applied on top of the solar cell, we also focus on proper interpretation and comparison of the measured and the simulated results, motivated by the conclusions from the previous section.
Using the combined optical model CROWM, we first simulated the organic solar cell (OSC) as presented in Fig. 1 without the MLA, i.e. all interfaces assumed perfectly flat. The complex refractive indices of the materials were taken as determined by the RT method, with the exception of the Ca and Ag which were taken from literature [25,26]. The simulated total absorptance within the photoactive pDPP5T-2:PC60BM absorber layer is plotted in Fig. 9(a) (black line). Also plotted in Fig. 9(a) is the measured EQE curve (black symbols). The absolute values of the two curves, A and EQE, differ significantly due to the effects of exciton and charge-carrier recombination, limited charge-carrier extraction, etc. However, since these effects are mostly independent on the wavelength, the shapes of the two curves should in principle be similar. From the results plotted in Fig. 9(a) we can see that indeed the simulated A reproduces the trends of the measured EQE very well. Finally, by applying the standard AM1.5 spectrum to the measured EQE and simulated A results, we can calculate the realistic and the ideal short-circuit current density, JSC,real and JSC, respectively. For the case of the flat organic solar cell without the MLA, we obtained JSC,real = 12.93 mA/cm2 from the measured EQE and JSC = 17.26 mA/cm2 from the simulated absorptance.
Fig. 9 (a) Measured external quantum efficiency and simulated absorptance in the pDPP5T-2:PC60BM absorber layer of bare organic solar cell (black) and solar cell with the MLA on top (red). The dashed blue line shows simulation results when infinite geometry is assumed. (b) Simulated JSC discrepancy relative to the infinite-size device as a function of the active area scaling factor (proportional area scaling in both dimensions assumed).
As the next step, we simulated the organic solar cell with the MLA applied on top of the front glass substrate, as shown in Fig. 1. As before, we initially assumed an infinite-sized uniformly illuminated cell. The simulated absorptance within the absorber layer is plotted in Fig. 9(a) (blue dashed line). From this result, we can calculate JSC = 20.69 mA/cm2, which presents an increase of 19.9% compared to the cell without the MLA. This substantial boost in the solar cell performance, however, cannot be observed from the measured EQE of the cell with the MLA that is also plotted in Fig. 9(a) (red symbols). In this case, we obtain JSC,real = 13.77 mA/cm2, which is only a 6.5% increase compared to the bare cell. Without further investigation, two (false) conclusions could be drawn from these results: first, the application of the MLA on top of the solar cell in reality only weakly improves the JSC of the cell, and second, the beneficial effects of the MLA are greatly overestimated by the optical simulations. Both conclusions, however, are incorrect, as will be demonstrated in the following.
The illustration in Fig. 7(b) shows schematically the optical situation of measuring the EQE of the organic solar cell with the MLA applied on top of the front glass substrate (for simplicity, the MLA and the glass substrate are shown as a single layer). The illustration demonstrates that due to the pronounced scattering at the front textured surface and a limited size of the back contact/reflector, especially in small-area laboratory cells, a substantial amount of light can be lost by propagating past the area of the solar cell. Since the lost light cannot efficiently contribute to the photocurrent, it is important to understand that the measured EQE values can be significantly lower than what they would be in the case of an up-scaled large-area solar cell (i.e. photovoltaic module). However, as was the case in the MLA measurements using the integrating sphere, it is difficult to experimentally determine the amount of these optical losses.
Therefore, to investigate the extent to which the limited cell size influences the A and EQE results, we turn again to optical modelling. For this purpose, we repeated the simulation of the organic solar cell with the MLA by taking the size of the incident beam, the size of the MLA sample, and the size of the back contact (4 x 6 mm) into account. The simulated A within the absorber layer obtained in this realistic case is plotted in Fig. 9 as thick red line. Compared to the infinite-area simulation, the curve is suppressed significantly. The JSC = 18.92 mA/cm2 can now be calculated, which presents an increase of 9.6% compared to the bare cell. This is much closer to the increase that was observed from the measurements, which means that the optical losses due to the geometry constraints of the measurement system are reproduced well by the simulations. By comparing the results of the simulations only, we can see that the effects of the limited cell size lead to a decrease (error) of JSC of about 8.6%. If we apply this figure to the measurements, we can now estimate the realistic JSC,real that would be obtained experimentally in the case of a realistic up-scaled large-area device (module): JSC,real = 15.07 mA/cm2, which is a boost of 16.6% compared to the realistic solar cell without the MLA. This result reveals the true potential of light management using the MLA in organic solar cells, which was initially obscured by the artifacts of the EQE measurement system employed for small-area solar cells.
Further on, we investigated how changing the active area of the solar cell affects the JSC discrepancy (error) relative to the infinite-size device. In general, this dependency is influenced not only by the area itself, but also by the aspect ratio of the area, the total thickness of the cell, the optical properties of the materials, the texture of the MLA, as well as the dimensions of the incident beam. The latter is especially important as it can vary between different measurement systems, even if the device itself is not changed. For example, a solar simulator typically illuminates an area that is much larger than the measured solar cell, whereas the collimated beam of a monochromator is typically smaller or equal to the area of the device. Since the purpose of our simulations is to focus on the artifacts introduced by the EQE measurement system, we only increased the area of the cell in the simulations (proportionally in both dimensions), while keeping all other parameters unchanged. The results presented in Fig. 9(b) show that in order to reduce the JSC error below 1%, at least a 1.9x larger device would be required (i.e. 5.5 mm x 8.3 mm), whereas at least a 40x larger device (i.e. 25.3 mm x 37.9 mm) would be required to reduce the error below 0.1%.
Finally, it should be noted that full consideration of the limited device area is also important for acquisition of the true internal quantum efficiency of textured organic solar cells: IQE = EQE/(1–R–Aparasitic) [27]. In this respect, the presented optical modelling technique can be employed not only to determine the parasitic absorptance in the supporting layers, Aparasitic, but also to account for the amount of optical losses introduced by the limited device area when measuring the EQE and the total reflectance, R, of the solar cell.
4.4 Evaluation of the optical gains and losses
Optical simulations were further employed to understand the mechanisms by which the MLA improves the performance of the organic solar cell, and also to identify the origins of the optical losses. For this purpose, we assumed an ideal infinite-size geometry in this case and performed simulations in several steps. Each step involves simulation of a partial structure that enables independent evaluation of each of the specific light management mechanism: (i) improved in-coupling, (ii) prolonged optical paths due to refraction, and (iii) light trapping (see further). The results of each simulation, i.e. the wavelength-dependent total reflectance, R, the total transmittance, T, and the absorptance within each layer of the simulated device, A, were weighted by the AM1.5 solar spectrum and integrated over the entire wavelength range of 350 – 900 nm. This way, we obtained the distribution of the total available JSC potential carried by the solar spectrum (JSC,total = 33.6 mA/cm2) among different parts of the simulated device.
First, we investigated the efficiency of light in-coupling into the solar cell. For this purpose, we were interested only in light propagation through the front part of the solar cell, and therefore we set the absorber layer as the medium in transmission. This “partial structure A” is indicated in Fig. 1. Two simulations with and without the MLA were performed, the selected results are presented in Fig. 10 (left section). The results show that the MLA reduces the amount of JSC losses due to reflection from the front part of the solar cell from 7.27% to 2.38%. At the same time, it increases the amount of JSC potential transmitted into the absorber layer from 83.04% to 85.77%. This improvement, however, is lower compared to the decrease of reflection losses. The reason is that due to light scattering (refraction) at the MLA, optical absorption in the front layers of the solar cell (especially ITO and PEDOT:PSS) is also increased. Therefore, it can be concluded that the anti-reflective (AR) property of the MLA, while beneficial, is not the dominant factor that enables improved performance of the organic solar cell, as optical transmission of the incident light into the absorber layer is only marginally improved.
Fig. 10 Distribution of the short-circuit current density potential among R, A, and T in different simulated structures with and without the MLA.
Next, we included the full 135 nm thick absorber layer into simulations, while keeping the absorber material as the medium in transmission. This “partial structure B” is also indicated in Fig. 1. The results of simulations with and without the MLA are presented in Fig. 10 (middle section). Most notably, the results reveal that more than half of the JSC potential transmitted into the absorber layer cannot be extracted during the first passing of the light through the 135 nm thick layer. Further on, it can be observed that the MLA improves the amount of JSC potential that can be extracted by absorption in the absorber layer, although the improvement is modest; from 34.11% to 37.43%. This improvement can be associated with the ability of the MLA to scatter (refract) light into larger angles of propagation, as can be seen from the calculated AID that is for this case plotted in Fig. 8 for the selected wavelength λ = 700 nm (red line). Larger angles of propagation prolong the effective optical paths through the absorber layer and, thus, increase the amount of extracted JSC potential.
Finally, we return to simulations of the complete organic solar cells with and without the MLA. The selected results are presented in Fig. 10 (right section). First, it is evident that the efficient Ca/Ag back reflector completely eliminates optical losses due to transmission through the structure. Instead, we observe a significant boost in the amount of the extracted JSC potential in the absorber layer (the area of the bar above the white separator line). However, efficient reflection at the back side also results in an increased amount of optical losses at the front side, both due to the light escaping out of the device (i.e. reflection from the complete solar cell structure), as well as due to optical absorption in the front layers (especially ITO and PEDOT:PSS). In the case of the bare solar cell without the MLA, these two origins of losses amount to 28.64% and 10.95% (not shown in the plot) of the total JSC potential, respectively. By applying the MLA on top of the solar cell, however, the losses due to reflection are reduced to 11.86%, while the losses due to absorption in the front layers are increased to 15.56%. Simulations reveal that this significant reduction of the reflection losses (relatively by 58.6%) is the most important mechanism that enables the relative 19.9% JSC boost in the organic solar cell, if the MLA is applied on top of the front glass substrate. Therefore, we concluded that the dominant light management function of the MLA is its ability to “trap” the reflected light by directing it back into the device.
4.5 Optimization of the absorber layer thickness
To demonstrate the usability of the calibrated optical model in a solar cell design process, we studied the role and optimized the thickness of the photoactive absorber layer, d, which is one of the most important parameters that influence the total JSC of the organic solar cell. In general, increasing the absorber layer thickness results in an increased JSC. At the same time, however, it also deteriorates the electrical properties of the solar cell, which reflects in a significant reduction of the fill factor, FF [16,28]. A typical realistic non-linear dependency FF vs. d (in-house measurements of realistic devices) is plotted in Fig. 11 as dashed blue line. It can be observed that the initial FF value of 69%, which is obtained for the absorber layer thickness d = 50 nm, drops to 45% by increasing the thickness to d = 200 nm. We simulated JSC for different d values and calculated the power conversion efficiency, PCE, by assuming a constant open-circuit voltage VOC = 0.6 V and the realistic FF as shown in Fig. 11. The results for the bare cell (black line) and the cell with the MLA (red line) are plotted in Fig. 11. Finally, for comparison, we also calculated PCE values by assuming a constant FF of 69% (no dependency on the absorber layer thickness); the results are also plotted in Fig. 11 (thin lines).
Fig. 11 The simulated power conversion efficiency of the bare organic solar cell (black) and the solar cell with the MLA on top (red) as a function of the absorber layer thickness, calculated for two cases: i) if assuming a constant fill factor of 69% (thin lines), and ii) if assuming realistic fill factor (thick lines). The realistic fill factor profile, which represents actual measured values of realistic solar cells, is plotted by the dashed blue line (right axis). The optimum power conversion efficiency points are also indicated.
The calculated PCE values presented in Fig. 11 reveal the influences of both dependencies mentioned above, JSC vs. d and FF vs. d. From the thin curves showing results for the constant FF, it is evident that an increasing JSC (as a result of an increasing absorber layer thickness) gradually raises PCE. Taking realistic FF into account, however, leads to a significant reduction of PCE at larger d values. Two distinct PCE maxima can be identified for both cases, and with them the optimal absorber layer thicknesses: for the bare solar cell, the highest PCE = 7.0% occurs at the optimal layer thickness d = 100 nm, while for the solar cell with the MLA, the highest PCE = 8.2% is enabled by the optimal d = 120 nm. The optimal thicknesses are in both cases defined by the balance of the positive effects imposed by d and the negative effects imposed by FF. Due to the larger overall JSC values enabled by the MLA, the balance is in this case reached at a larger absorber layer thickness, which is also to be expected in other cases in which light management techniques are employed to boost the short-circuit current density of the organic solar cell.
5. Conclusions
We presented in detail the process of advanced optical simulation and supporting experimental characterization of organic solar cells with a micro-textured light management foil applied on top of the front glass substrate. Using the upgraded combined optical model CROWM, we first identified the artifacts of the employed measurement systems that are caused by geometry constraints of the systems. We demonstrated that accurate evaluation of their influence on the measurement results is crucial for proper interpretation of the results that could otherwise lead to false conclusions. Thus, we were able to estimate that the analysed micro-textured light management foil applied on top of a realistic large-area organic PV module would enable a more than 16% increase of the short-circuit current density, although the measurements of a single small-area solar cell indicated an increase of mere 6.5%, due to artifacts of the measurement system.
Using the combined optical model, we further investigated the light management properties of the analysed micro-textured foil. Simulations revealed that reduced reflection from the front surface as well as prolonged optical paths through the absorber layer enabled by scattering (refraction), while beneficial, have only moderate impact on the performance of the solar cell. Instead, we found out that the ability of the foil to prevent the backward-propagating light from escaping out of the cell at the front side is the dominant light-trapping mechanism. With all mechanisms combined, the total reflectance from the solar cell can be reduced by nearly 60%, while the short-circuit current density can be improved by almost 20%.
Finally, we analysed the dependence of the power conversion efficiency on the thickness of the absorber layer of the organic solar cell. For this purpose, we took realistic open-circuit voltage and fill factor values into account. Simulations reveal clear optimal points of power conversion efficiency for both the bare cell (PCE = 7.0% @ d = 100 nm) as well as for the cell with the light-management foil (PCE = 8.2% @ d = 120 nm). The shift between the two optimal thicknesses is attributed to the larger short-circuit current densities enabled by the light-management foil applied on top of the organic solar cell.
It should be noted that although the present work was focused on the organic solar cells enhanced with micro-textured foils, we believe the methodology and the conclusions presented in this paper are relevant also for many other photovoltaic technologies, including perovskite solar cells, and also for situations where efficient light scattering is introduced by other means, including by natural polycrystallinity of the material.
Funding
Slovenian Research Agency (P2-0197, J2-5466); EU project SOLPROCEL – “Solution processed high performance transparent organic photovoltaic cells” (604506); “Aufbruch Bayern” initiative of the state of Bavaria; China Scholarship Council.
Acknowledgments
The authors acknowledge the use of the services and facilities of the “Energie Campus Nürnberg” (EnCn).
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